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June 16th, 2010, 05:57 PM   #1
 
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The range of a matrix transformation

How to do you determine if a vector (w) is in the range a matrix transformation.

Let f: R^2 --> R^3
f(x) = Ax



Vector w


Why is it a no?
My work: ( I don't know if I'm doing it right)




and why is for Vector w, it's a yes?




The book says that the set of all images of the vectors in R^n is called the range of f. I don't know what it means. Can someone please explain to me how to determine the range. Thanks in advance
remeday86 is offline  
 
June 16th, 2010, 07:21 PM   #2
 
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Re: The range of a matrix transformation

You want w= f(v) = Av, where v is a vector .

The equation should be:



You cannot substitute values of w into v, you need to see if any value of v, when multiplied by A gives you w. See if there is any v=[x,y] which satisfies this equation.

Edit: Some clarification. "The set of all images" is the set . So, if w is in the image, w=f(v) for some vector v in R^2. To check if such a vector exists, see if there is any vector which satisfies f(v)=w.
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